9780028242866

Advanced Mathematical Concepts

by ; ; ;
  • ISBN13:

    9780028242866

  • ISBN10:

    0028242866

  • Format: Hardcover
  • Copyright: 1997-01-01
  • Publisher: Glencoe/McGraw-Hill School Pub Co

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Table of Contents

Unit 1 Relations, Functions, and Graphs 2(236)
Linear Relations and Functions
4(48)
Relations and Functions
6(6)
Case Study Follow-Up
11(1)
Composition and Inverses of Functions
12(9)
Graphing Calculators: Graphics Linear Equations and Inequalities
19(2)
Linear Functions and Inequalities
21(8)
Mid-Chapter Review
27(1)
Technology: Graphing Linear Relations
28(1)
Distance and Slope
29(7)
Forms of Linear Equations
36(6)
Parallel and Perpendicular Lines
42(10)
Decision Making: Recycling
47(1)
Chapter Summary and Review
48(3)
Chapter Test
51(1)
Systems of Equations and Inequalities
52(50)
Graphing Calculators: Graphing Systems of Linear Equations
54(2)
Solving Systems of Equations
56(8)
Graphing Calculators: Matrices
62(2)
Introduction to Matrices
64(7)
Decision Making: Choosing a College Major
70(1)
Determinants and Multiplicative Inverses of Matrices
71(8)
Mid-Chapter Review
77(1)
Technology: Finding Determinants of Matrices
78(1)
Solving Systems of Equations by Using Matrices
79(7)
Graphing Calculators: Graphing Systems of Linear Inequalities
84(2)
Solving Systems of Inequalities
86(5)
Linear Programming
91(11)
Case Study Follow-Up
97(1)
Chapter Summary and Review
98(3)
Chapter Test
101(1)
The Nature of Graphs
102(74)
Graphing Calculators: Graphing Polynomial Functions
104(2)
Symmetry
106(11)
Decision Making: The Ozone Layer
116(1)
Families of Graphs
117(9)
Graphing Calculators: Graphing Radical Functions
125(1)
Inverse Functions and Relations
126(8)
Graphing Calculators: Graphing Rational Functions
132(2)
Rational Functions and Asymptotes
134(10)
Technology: Graphing Rational Functions
143(1)
Graphs of Inequalities
144(5)
Mid-Chapter Review
148(1)
Tangent to a Curve
149(7)
Graphing Calculators: Locating Critical Points of Polynomial Functions
155(1)
Graphs and Critical Points of Polynomial Functions
156(8)
Case Study Follow-Up
163(1)
Continuity and End Behavior
164(12)
Chapter Summary and Review
172(3)
Chapter Test
175(1)
Polynomial and Rational Functions
176(60)
Polynomial Functions
178(9)
Case Study Follow-Up
184(1)
Graphing Calculators: Graphing Quadratic Functions
185(2)
Quadratic Equations and Inequalities
187(8)
Decision Making: Choosing a Vacation Spot
194(1)
The Remainder and Factor Theorems
195(6)
The Rational Root Theorem
201(8)
Mid-Chapter Review
207(1)
Graphing Calculators: Locating Zeros of Polynomial Functions
208(1)
Locating the Zeros of a Function
209(7)
Technology: Locating Zeros and Critical Points
215(1)
Rational Equations and Partial Fractions
216(9)
Graphing Calculators: Solving Radical Equations and Inequalities
223(2)
Radical Equations and Inequalties
225(11)
Chapter Summary and Review
230(3)
Chapter Test
233(1)
Unit 1 Review
234(2)
Unit 2 Trigonometry 236(226)
The Trigonometric Functions
238(62)
Angles and Their Measure
240(7)
Central Angles and Arcs
247(8)
Decision Making: Education and Literacy
254(1)
Circular Functions
255(8)
Mid-Chapter Review
262(1)
Trigonometric Functions of Special Angles
263(6)
Right Triangles
269(7)
Case Study Follow-Up
275(1)
The Law of Sines
276(7)
Technology: Solving Triangles
282(1)
The Law of Cosines
283(5)
Area of Triangles
288(12)
Chapter Summary and Review
296(3)
Chapter Test
299(1)
Graphs and Inverses of the Trigonometric Functions
300(56)
Graphs of the Trigonometric Functions
302(7)
Decision Making: Drunk Driving
307(1)
Technology: Ordered Pairs for Graphing Trigonometric Functions
308(1)
Amplitude, Period, and Phase Shift
309(12)
Case Study Follow-Up
318(1)
Graphing Calculators: Graphing Trigonometric Functions
319(2)
Graphing Trigonometric Functions
321(7)
Inverse Trigonometric Functions
328(6)
Mid-Chapter Review
333(1)
Principal Values of the Inverse Trigonometric Functions
334(6)
Graphing Calculators: Graphing Inverses of Trigonometric Functions
339(1)
Graphing Inverses of Trigonometric Functions
340(5)
Simple Harmonic Motion
345(11)
Chapter Summary and Review
352(3)
Chapter Test
355(1)
Trigonometric Identities and Equations
356(54)
Basic Trigonometric Identities
358(6)
Verifying Trigonometric Identities
364(7)
Graphing Calculators: Verifying Trigonometric Identities
369(2)
Sum and Difference Identities
371(6)
Double-Angle and Half-Angle Identities
377(10)
Mid-Chapter Review
383(1)
Technology: Double and Half Angles
384(1)
Graphing Calculators: Solving Trigonometric Equations
385(2)
Solving Trigonometric Equations
387(5)
Case Study Follow-Up
391(1)
Normal Form of a Linear Equation
392(6)
Decision Making: Writing a Budget
397(1)
Distance from a Point to a Line
398(12)
Chapter Summary and Review
406(3)
Chapter Test
409(1)
Vectors and Parametric Equations
410(52)
Geometric Vectors
412(7)
Algebraic Vectors
419(6)
Decision Making: Choosing a Used Car
424(1)
Vectors in Three-Dimensional Space
425(5)
Perpendicular Vectors
430(6)
Mid-Chapter Review
435(1)
Applications with Vectors
436(6)
Case Study Follow-Up
441(1)
Vectors and Parametric Equations
442(7)
Technology: Using Parametric Equations
448(1)
Using Parametric Equations to Model Motion
449(13)
Chapter Summary and Review
456(3)
Chapter Test
459(1)
Unit 2 Review
460(2)
Unit 3 Advanced Functions and Graphing 462(190)
Polar Coordinates and Complex Numbers
464(58)
Polar Coordinates
466(9)
Decision Making: The Budget Deficit
472(1)
Graphing Calculators: Graphing Polar Equations
473(2)
Graphs of Polar Equations
475(8)
Case Study Follow-Up
481(1)
Technology: Graphing Polar Equations
482(1)
Polar and Rectangular Coordinates
483(5)
Polar Form of a Linear Function
488(6)
Mid-Chapter Review
493(1)
Simplifying Complex Numbers
494(7)
Polar Form of Complex Numbers
501(5)
Products and Quotients of Complex Numbers in Polar Form
506(4)
Powers and Roots of Complex Numbers
510(12)
Chapter Summary and Review
518(3)
Chapter Test
521(1)
Conics
522(74)
The Circle
524(10)
Decision Making: Choosing a Home Computer
532(1)
Graphing Calculators: Locating the Vertex of a Parabola
533(1)
The Parabola
534(8)
The Ellipse
542(9)
Case Study Follow-Up
550(1)
The Hyperbola
551(10)
Mid-Chapter Review
559(1)
Technology: Asymptotes of a Hyperbola
560(1)
Conic Sections
561(9)
Graphing Calculators: Conic Sections
568(2)
Transformations of Conics
570(9)
Graphing Calculators: Solving Quadratic Systems
577(2)
Systems of Second-Degree Equations and Inequalities
579(6)
Tangents and Normals to the Conic Sections
585(11)
Chapter Summary and Review
592(3)
Chapter Test
595(1)
Exponential and Logarithmic Functions
596(56)
Rational Exponents
598(8)
Decision Making: Homelessness
604(1)
Graphing Calculators: Graphing Exponential Functions
605(1)
Exponential Functions
605(1)
Exponential Functions
606(8)
The Number e
614(8)
Case Study Follow-Up
619(1)
Technology: Compound Interest
620(1)
Graphing Calculators: Graphing Logarithmic Functions
621(1)
Logarithmic Functions
621(1)
Logarithmic Functions
622(7)
Mid-Chapter Review
628(1)
Common Logarithms
629(7)
Graphing Calculators: Exponential and Logarithmic Equations and Inequalities
634(2)
Exponential and Logarithmic Equations
636(5)
Natural Logarithms
641(11)
Chapter Summary and Review
646(3)
Chapter Test
649(1)
Unit 3 Review
650(2)
Unit 4 Discrete Mathematics 652(258)
Sequences and Series
654(56)
Arithmetic Sequences and Series
656(7)
Case Study Follow-Up
662(1)
Geometric Sequences and Series
663(8)
Technology: Amortization
670(1)
Infinite Sequences and Series
671(8)
Decision Making: Finding Money for College
678(1)
Convergent and Divergent Series
679(6)
Mid-Chapter Review
684(1)
Sigma Notation and the nth Term
685(6)
The Binomial Theorem
691(5)
Special Sequences and Series
696(6)
Mathematical Induction
702(8)
Chapter Summary and Review
706(3)
Chapter Test
709(1)
Iteration and Fractals
710(40)
Iterating Functions with Real Numbers
712(5)
Graphical Iteration of Linear Functions
717(5)
Graphical Iteration of the Logistic Function
722(8)
Mid-Chapter Review
728(1)
Technology: Graphical Iteration
729(1)
Complex Numbers and Iteration
730(4)
Decision Making: Crime
733(1)
Escape Points, Prisoner Points, and Julia Sets
734(6)
The Mandelbrot Set
740(10)
Case Study Follow-Up
745(1)
Chapter Summary and Review
746(3)
Chapter Test
749(1)
Combinatorics and Probability
750(50)
Permutations
752(6)
Decision Making: Choosing Car Insurance
757(1)
Permutations with Repetitions and Circular Permutations
758(6)
Combinations
764(4)
Mid-Chapter Review
767(1)
Probability and Odds
768(6)
Case Study Follow-Up
773(1)
Probabilities of Independent and Dependent Events
774(5)
Probabilities of Mutually Exclusive or Inclusive Events
779(5)
Conditional Probability
784(6)
The Binomial Theorem and Probability
790(10)
Technology: Dice Roll Simulation
795(1)
Chapter Summary and Review
796(3)
Chapter Test
799(1)
Statistics and Data Analysis
800(64)
The Frequency Distribution
802(9)
Decision Making: Car Airbags
810(1)
Measures of Central Tendency
811(9)
Measures of Variability
820(10)
Case Study Follow-Up
829(1)
The Normal Distribution
830(8)
Mid-Chapter Review
837(1)
Sample Sets of Data
838(8)
Graphing Calculators: Scatter Plots and Lines of Regression
844(2)
Scatter Plots
846(18)
Technology: Median-Fit Lines
855(1)
Graphing Calculators: Curve Fitting
856(4)
Chapter Summary and Review
860(3)
Chapter Test
863(1)
Graph Theory
864(46)
Graphs
866(6)
Walks and Paths
872(5)
Euler Paths and Circuits
877(6)
Mid-Chapter Review
882(1)
Shortest Paths and Minimal Distances
883(7)
Case Study Follow-Up
889(1)
Trees
890(6)
Decision Making: Planning a Party
895(1)
Graphs and Matrices
896(14)
Chapter Summary and Review
904(3)
Chapter Test
907(1)
Unit 4 Review
908(2)
Unit 5 An Introduction to Calculus 910(46)
Limits, Derivatives, and Integrals
912(44)
Limits
914(9)
Derivatives and Differentiation Techniques
923(8)
Case Study Follow-Up
930(1)
Area Under a Curve
931(8)
Mid-Chapter Review
937(1)
Technology: Riemann Sums
938(1)
Integration
939(6)
The Fundamental Theorem of Calculus
945(11)
Decision Making: Planning a Move
951(1)
Chapter Summary and Review
952(3)
Chapter Test
955(1)
Case Studies 956(14)
Symbols 970(1)
Formulas 971(1)
Glossary 972(7)
Selected Answers 979(35)
Index 1014(9)
Photo Credits 1023

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